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The renormalization group method in statistical hydrodynamics. (English) Zbl 0830.76042
This paper gives a first principles formulation of a renormalization group (RG) method appropriate to study of turbulence in incompressible fluids governed by Navier-Stokes equations. The present method is a momentum-shell RG of Kadanoff-Wilson type based upon the Martin-Siggia- Rose field-theory formulation of stochastic dynamics. A simple set of diagrammatic rules are developed which are exact within perturbation theory (unlike the well-known Ma-Mazenko prescriptions). It is also shown that the claim of V. Yakhot and S. A. Orszag [J. Sci. Comput. 1, 3-51 (1986; Zbl 0648.76040)] is false and that higher-order terms are irrelevant in the \(\varepsilon\) expansion \(RG\) for randomly forced Navier-Stokes equations with power-law force spectrum.

MSC:
76F99 Turbulence
76D05 Navier-Stokes equations for incompressible viscous fluids
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